Spatial coherency and amplification effects of ground motion with tunnel site based on multidimensional autoregressive model

Abstract

The traditional periodic diagram method is primarily used to solve ground motion coherence coefficients. However, in this method, power spectra need to be artificially smoothed, which will result in an abhorrent situation. To solve this key problem, this study uses the dynamic centrifuge model test results with a circular tunnel completed by Schofield Centre (University of Cambridge) as the basic data. The multidimensional autoregressive (AR) model is used to replace the periodic diagram method for computation, and its rationality is evaluated and verified from many perspectives. The difference between the results of the two methods under the condition of tunnel sites in multiple dimensions is discussed from the perspectives of the reconstruction effect, coherence coefficient, and the site amplification effect of records. The results are as follows: The multidimensional AR model can realize the accurate reconstruction of strong motion acceleration records. The coherence coefficient calculated by the AR model is generally smoother than that calculated by the periodic diagram method, which is conducive to fitting and inducing the parameters of empirical models in subsequent research. Under EQ1–EQ4, the ground motion amplification coefficient of each vibration mode first decreases and then increases from the base to the surface. The AR model is more effective than the periodic diagram method in reflecting the importance of the influence of higher-order modes on site amplification.